LMFDB - Embedded newform 960.2.bl.a.49.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(49,960)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("960.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bl (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			49.15
Character	$\chi$	$=$	960.49
Dual form			960.2.bl.a.529.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(-2.06370 + 0.860885i) q^{5} -0.707398 q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(-2.06370 + 0.860885i) q^{5} -0.707398 q^{7} +1.00000i q^{9} +(-1.79993 - 1.79993i) q^{11} +(3.86348 + 3.86348i) q^{13} +(-2.06800 - 0.850522i) q^{15} +0.244884i q^{17} +(-1.53863 + 1.53863i) q^{19} +(-0.500206 - 0.500206i) q^{21} -6.92280 q^{23} +(3.51775 - 3.55323i) q^{25} +(-0.707107 + 0.707107i) q^{27} +(-4.89882 + 4.89882i) q^{29} -7.60734 q^{31} -2.54548i q^{33} +(1.45986 - 0.608988i) q^{35} +(-8.47863 + 8.47863i) q^{37} +5.46378i q^{39} -2.12118i q^{41} +(0.684507 - 0.684507i) q^{43} +(-0.860885 - 2.06370i) q^{45} -4.47342i q^{47} -6.49959 q^{49} +(-0.173159 + 0.173159i) q^{51} +(1.47026 - 1.47026i) q^{53} +(5.26405 + 2.16499i) q^{55} -2.17595 q^{57} +(-5.86121 - 5.86121i) q^{59} +(0.0537432 - 0.0537432i) q^{61} -0.707398i q^{63} +(-11.2991 - 4.64706i) q^{65} +(7.85550 + 7.85550i) q^{67} +(-4.89516 - 4.89516i) q^{69} -2.08595i q^{71} +9.69951 q^{73} +(4.99994 - 0.0250827i) q^{75} +(1.27326 + 1.27326i) q^{77} +7.34690 q^{79} -1.00000 q^{81} +(6.80291 + 6.80291i) q^{83} +(-0.210817 - 0.505369i) q^{85} -6.92797 q^{87} +3.07483i q^{89} +(-2.73301 - 2.73301i) q^{91} +(-5.37920 - 5.37920i) q^{93} +(1.85069 - 4.49986i) q^{95} +1.39922i q^{97} +(1.79993 - 1.79993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{19} + 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} + 16 q^{61} + 16 q^{65} - 16 q^{69} + 16 q^{75} + 96 q^{79} - 48 q^{81} + 32 q^{91} + 48 q^{95}+O(q^{100}) $ 48 * q - 8 * q^19 + 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 + 16 * q^61 + 16 * q^65 - 16 * q^69 + 16 * q^75 + 96 * q^79 - 48 * q^81 + 32 * q^91 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	−2.06370	+	0.860885i	−0.922917	+	0.385000i
$5$	−2.06370	+	0.860885i	−0.922917	+	0.385000i
$6$		0			0
$7$	−0.707398			−0.267371			−0.133686	−	0.991024i	$-0.542681\pi$
$7$	−0.707398			−0.267371			−0.133686	+	0.991024i	$0.542681\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−1.79993	−	1.79993i	−0.542699	−	0.542699i	0.381621	−	0.924319i	$-0.375366\pi$
$11$	−1.79993	−	1.79993i	−0.542699	−	0.542699i	−0.924319	+	0.381621i	$0.875366\pi$
$12$		0			0
$13$	3.86348	+	3.86348i	1.07154	+	1.07154i	0.997236	+	0.0742996i	$0.0236721\pi$
$13$	3.86348	+	3.86348i	1.07154	+	1.07154i	0.0742996	+	0.997236i	$0.476328\pi$
$14$		0			0
$15$	−2.06800	−	0.850522i	−0.533955	−	0.219604i
$16$		0			0
$17$			0.244884i			0.0593932i	0.999559	+	0.0296966i	$0.00945410\pi$
$17$			0.244884i			0.0593932i	−0.999559	+	0.0296966i	$0.990546\pi$
$18$		0			0
$19$	−1.53863	+	1.53863i	−0.352986	+	0.352986i	−0.861219	−	0.508233i	$-0.830299\pi$
$19$	−1.53863	+	1.53863i	−0.352986	+	0.352986i	0.508233	+	0.861219i	$0.330299\pi$
$20$		0			0
$21$	−0.500206	−	0.500206i	−0.109154	−	0.109154i
$22$		0			0
$23$	−6.92280			−1.44350			−0.721752	−	0.692152i	$-0.756663\pi$
$23$	−6.92280			−1.44350			−0.721752	+	0.692152i	$0.756663\pi$
$24$		0			0
$25$	3.51775	−	3.55323i	0.703551	−	0.710645i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	−4.89882	+	4.89882i	−0.909688	+	0.909688i	−0.996247	−	0.0865591i	$-0.972413\pi$
$29$	−4.89882	+	4.89882i	−0.909688	+	0.909688i	0.0865591	+	0.996247i	$0.472413\pi$
$30$		0			0
$31$	−7.60734			−1.36632			−0.683159	−	0.730270i	$-0.739394\pi$
$31$	−7.60734			−1.36632			−0.683159	+	0.730270i	$0.739394\pi$
$32$		0			0
$33$		−	2.54548i		−	0.443112i
$34$		0			0
$35$	1.45986	−	0.608988i	0.246761	−	0.102938i
$36$		0			0
$37$	−8.47863	+	8.47863i	−1.39388	+	1.39388i	−0.577459	+	0.816420i	$0.695956\pi$
$37$	−8.47863	+	8.47863i	−1.39388	+	1.39388i	−0.816420	+	0.577459i	$0.804044\pi$
$38$		0			0
$39$			5.46378i			0.874905i
$40$		0			0
$41$		−	2.12118i		−	0.331272i	−0.986187	−	0.165636i	$-0.947032\pi$
$41$		−	2.12118i		−	0.331272i	0.986187	−	0.165636i	$-0.0529677\pi$
$42$		0			0
$43$	0.684507	−	0.684507i	0.104386	−	0.104386i	−0.652985	−	0.757371i	$-0.726483\pi$
$43$	0.684507	−	0.684507i	0.104386	−	0.104386i	0.757371	+	0.652985i	$0.226483\pi$
$44$		0			0
$45$	−0.860885	−	2.06370i	−0.128333	−	0.307639i
$46$		0			0
$47$		−	4.47342i		−	0.652515i	−0.945281	−	0.326258i	$-0.894212\pi$
$47$		−	4.47342i		−	0.652515i	0.945281	−	0.326258i	$-0.105788\pi$
$48$		0			0
$49$	−6.49959			−0.928513
$50$		0			0
$51$	−0.173159	+	0.173159i	−0.0242472	+	0.0242472i
$52$		0			0
$53$	1.47026	−	1.47026i	0.201956	−	0.201956i	−0.598881	−	0.800838i	$-0.704388\pi$
$53$	1.47026	−	1.47026i	0.201956	−	0.201956i	0.800838	+	0.598881i	$0.204388\pi$
$54$		0			0
$55$	5.26405	+	2.16499i	0.709804	+	0.291927i
$56$		0			0
$57$	−2.17595			−0.288212
$58$		0			0
$59$	−5.86121	−	5.86121i	−0.763065	−	0.763065i	0.213810	−	0.976875i	$-0.431413\pi$
$59$	−5.86121	−	5.86121i	−0.763065	−	0.763065i	−0.976875	+	0.213810i	$0.931413\pi$
$60$		0			0
$61$	0.0537432	−	0.0537432i	0.00688112	−	0.00688112i	−0.703658	−	0.710539i	$-0.748451\pi$
$61$	0.0537432	−	0.0537432i	0.00688112	−	0.00688112i	0.710539	+	0.703658i	$0.248451\pi$
$62$		0			0
$63$		−	0.707398i		−	0.0891237i
$64$		0			0
$65$	−11.2991	−	4.64706i	−1.40148	−	0.576397i
$66$		0			0
$67$	7.85550	+	7.85550i	0.959702	+	0.959702i	0.999219	−	0.0395170i	$-0.0125819\pi$
$67$	7.85550	+	7.85550i	0.959702	+	0.959702i	−0.0395170	+	0.999219i	$0.512582\pi$
$68$		0			0
$69$	−4.89516	−	4.89516i	−0.589308	−	0.589308i
$70$		0			0
$71$		−	2.08595i		−	0.247557i	−0.992310	−	0.123778i	$-0.960499\pi$
$71$		−	2.08595i		−	0.247557i	0.992310	−	0.123778i	$-0.0395012\pi$
$72$		0			0
$73$	9.69951			1.13524			0.567621	−	0.823290i	$-0.307864\pi$
$73$	9.69951			1.13524			0.567621	+	0.823290i	$0.307864\pi$
$74$		0			0
$75$	4.99994	−	0.0250827i	0.577343	−	0.00289630i
$76$		0			0
$77$	1.27326	+	1.27326i	0.145102	+	0.145102i
$78$		0			0
$79$	7.34690			0.826591			0.413295	−	0.910597i	$-0.364378\pi$
$79$	7.34690			0.826591			0.413295	+	0.910597i	$0.364378\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	6.80291	+	6.80291i	0.746716	+	0.746716i	0.973861	−	0.227145i	$-0.0729391\pi$
$83$	6.80291	+	6.80291i	0.746716	+	0.746716i	−0.227145	+	0.973861i	$0.572939\pi$
$84$		0			0
$85$	−0.210817	−	0.505369i	−0.0228663	−	0.0548149i
$86$		0			0
$87$	−6.92797			−0.742757
$88$		0			0
$89$			3.07483i			0.325931i	0.986632	+	0.162966i	$0.0521060\pi$
$89$			3.07483i			0.325931i	−0.986632	+	0.162966i	$0.947894\pi$
$90$		0			0
$91$	−2.73301	−	2.73301i	−0.286498	−	0.286498i
$92$		0			0
$93$	−5.37920	−	5.37920i	−0.557797	−	0.557797i
$94$		0			0
$95$	1.85069	−	4.49986i	0.189877	−	0.461676i
$96$		0			0
$97$			1.39922i			0.142070i	0.997474	+	0.0710348i	$0.0226301\pi$
$97$			1.39922i			0.142070i	−0.997474	+	0.0710348i	$0.977370\pi$
$98$		0			0
$99$	1.79993	−	1.79993i	0.180900	−	0.180900i
$100$		0			0
$101$	11.7916	+	11.7916i	1.17331	+	1.17331i	0.981415	+	0.191895i	$0.0614633\pi$
$101$	11.7916	+	11.7916i	1.17331	+	1.17331i	0.191895	+	0.981415i	$0.438537\pi$
$102$		0			0
$103$	−2.29240			−0.225877			−0.112938	−	0.993602i	$-0.536026\pi$
$103$	−2.29240			−0.225877			−0.112938	+	0.993602i	$0.536026\pi$
$104$		0			0
$105$	1.46290	+	0.601657i	0.142764	+	0.0587157i
$106$		0			0
$107$	−9.49009	+	9.49009i	−0.917442	+	0.917442i	−0.996843	−	0.0794010i	$-0.974699\pi$
$107$	−9.49009	+	9.49009i	−0.917442	+	0.917442i	0.0794010	+	0.996843i	$0.474699\pi$
$108$		0			0
$109$	11.9058	−	11.9058i	1.14037	−	1.14037i	0.151984	−	0.988383i	$-0.451434\pi$
$109$	11.9058	−	11.9058i	1.14037	−	1.14037i	0.988383	−	0.151984i	$-0.0485662\pi$
$110$		0			0
$111$	−11.9906			−1.13810
$112$		0			0
$113$		−	7.92806i		−	0.745809i	−0.927870	−	0.372904i	$-0.878362\pi$
$113$		−	7.92806i		−	0.745809i	0.927870	−	0.372904i	$-0.121638\pi$
$114$		0			0
$115$	14.2866	−	5.95974i	1.33223	−	0.555748i
$116$		0			0
$117$	−3.86348	+	3.86348i	−0.357179	+	0.357179i
$118$		0			0
$119$		−	0.173231i		−	0.0158800i
$120$		0			0
$121$		−	4.52052i		−	0.410956i
$122$		0			0
$123$	1.49990	−	1.49990i	0.135241	−	0.135241i
$124$		0			0
$125$	−4.20068	+	10.3612i	−0.375721	+	0.926733i
$126$		0			0
$127$			19.4466i			1.72561i	0.505536	+	0.862806i	$0.331295\pi$
$127$			19.4466i			1.72561i	−0.505536	+	0.862806i	$0.668705\pi$
$128$		0			0
$129$	0.968040			0.0852311
$130$		0			0
$131$	0.354049	−	0.354049i	0.0309334	−	0.0309334i	−0.691471	−	0.722404i	$-0.743037\pi$
$131$	0.354049	−	0.354049i	0.0309334	−	0.0309334i	0.722404	+	0.691471i	$0.243037\pi$
$132$		0			0
$133$	1.08842	−	1.08842i	0.0943783	−	0.0943783i
$134$		0			0
$135$	0.850522	−	2.06800i	0.0732013	−	0.177985i
$136$		0			0
$137$	−7.30033			−0.623709			−0.311854	−	0.950130i	$-0.600950\pi$
$137$	−7.30033			−0.623709			−0.311854	+	0.950130i	$0.600950\pi$
$138$		0			0
$139$	8.85519	+	8.85519i	0.751087	+	0.751087i	0.974682	−	0.223595i	$-0.0717793\pi$
$139$	8.85519	+	8.85519i	0.751087	+	0.751087i	−0.223595	+	0.974682i	$0.571779\pi$
$140$		0			0
$141$	3.16319	−	3.16319i	0.266388	−	0.266388i
$142$		0			0
$143$		−	13.9080i		−	1.16304i
$144$		0			0
$145$	5.89239	−	14.3270i	0.489337	−	1.18980i
$146$		0			0
$147$	−4.59590	−	4.59590i	−0.379064	−	0.379064i
$148$		0			0
$149$	5.41385	+	5.41385i	0.443520	+	0.443520i	0.893193	−	0.449673i	$-0.148460\pi$
$149$	5.41385	+	5.41385i	0.443520	+	0.443520i	−0.449673	+	0.893193i	$0.648460\pi$
$150$		0			0
$151$		−	0.341548i		−	0.0277948i	−0.999903	−	0.0138974i	$-0.995576\pi$
$151$		−	0.341548i		−	0.0277948i	0.999903	−	0.0138974i	$-0.00442382\pi$
$152$		0			0
$153$	−0.244884			−0.0197977
$154$		0			0
$155$	15.6993	−	6.54904i	1.26100	−	0.526032i
$156$		0			0
$157$	−2.86465	−	2.86465i	−0.228624	−	0.228624i	0.583494	−	0.812118i	$-0.301685\pi$
$157$	−2.86465	−	2.86465i	−0.228624	−	0.228624i	−0.812118	+	0.583494i	$0.801685\pi$
$158$		0			0
$159$	2.07927			0.164897
$160$		0			0
$161$	4.89717			0.385951
$162$		0			0
$163$	5.94216	+	5.94216i	0.465426	+	0.465426i	0.900429	−	0.435003i	$-0.143253\pi$
$163$	5.94216	+	5.94216i	0.465426	+	0.465426i	−0.435003	+	0.900429i	$0.643253\pi$
$164$		0			0
$165$	2.19137	+	5.25312i	0.170598	+	0.408955i
$166$		0			0
$167$	−14.4595			−1.11891			−0.559454	−	0.828861i	$-0.688989\pi$
$167$	−14.4595			−1.11891			−0.559454	+	0.828861i	$0.688989\pi$
$168$		0			0
$169$			16.8529i			1.29638i
$170$		0			0
$171$	−1.53863	−	1.53863i	−0.117662	−	0.117662i
$172$		0			0
$173$	−6.65096	−	6.65096i	−0.505663	−	0.505663i	0.407529	−	0.913192i	$-0.366390\pi$
$173$	−6.65096	−	6.65096i	−0.505663	−	0.505663i	−0.913192	+	0.407529i	$0.866390\pi$
$174$		0			0
$175$	−2.48845	+	2.51354i	−0.188109	+	0.190006i
$176$		0			0
$177$		−	8.28901i		−	0.623040i
$178$		0			0
$179$	−17.2660	+	17.2660i	−1.29052	+	1.29052i	−0.356052	+	0.934466i	$0.615877\pi$
$179$	−17.2660	+	17.2660i	−1.29052	+	1.29052i	−0.934466	+	0.356052i	$0.884123\pi$
$180$		0			0
$181$	5.12242	+	5.12242i	0.380746	+	0.380746i	0.871371	−	0.490625i	$-0.163231\pi$
$181$	5.12242	+	5.12242i	0.380746	+	0.380746i	−0.490625	+	0.871371i	$0.663231\pi$
$182$		0			0
$183$	0.0760044			0.00561841
$184$		0			0
$185$	10.1983	−	24.7965i	0.749791	−	1.82308i
$186$		0			0
$187$	0.440774	−	0.440774i	0.0322326	−	0.0322326i
$188$		0			0
$189$	0.500206	−	0.500206i	0.0363846	−	0.0363846i
$190$		0			0
$191$	17.8040			1.28825			0.644124	−	0.764921i	$-0.277222\pi$
$191$	17.8040			1.28825			0.644124	+	0.764921i	$0.277222\pi$
$192$		0			0
$193$			17.2222i			1.23968i	0.784727	+	0.619842i	$0.212803\pi$
$193$			17.2222i			1.23968i	−0.784727	+	0.619842i	$0.787197\pi$
$194$		0			0
$195$	−4.70369	−	11.2756i	−0.336838	−	0.807465i
$196$		0			0
$197$	−10.0764	+	10.0764i	−0.717915	+	0.717915i	−0.968178	−	0.250263i	$-0.919483\pi$
$197$	−10.0764	+	10.0764i	−0.717915	+	0.717915i	0.250263	+	0.968178i	$0.419483\pi$
$198$		0			0
$199$		−	5.74179i		−	0.407025i	−0.979072	−	0.203513i	$-0.934764\pi$
$199$		−	5.74179i		−	0.407025i	0.979072	−	0.203513i	$-0.0652358\pi$
$200$		0			0
$201$			11.1094i			0.783593i
$202$		0			0
$203$	3.46541	−	3.46541i	0.243224	−	0.243224i
$204$		0			0
$205$	1.82609	+	4.37748i	0.127540	+	0.305737i
$206$		0			0
$207$		−	6.92280i		−	0.481168i
$208$		0			0
$209$	5.53885			0.383130
$210$		0			0
$211$	9.73318	−	9.73318i	0.670060	−	0.670060i	−0.287670	−	0.957730i	$-0.592881\pi$
$211$	9.73318	−	9.73318i	0.670060	−	0.670060i	0.957730	+	0.287670i	$0.0928806\pi$
$212$		0			0
$213$	1.47499	−	1.47499i	0.101065	−	0.101065i
$214$		0			0
$215$	−0.823339	+	2.00190i	−0.0561512	+	0.136529i
$216$		0			0
$217$	5.38141			0.365314
$218$		0			0
$219$	6.85859	+	6.85859i	0.463460	+	0.463460i
$220$		0			0
$221$	−0.946104	+	0.946104i	−0.0636419	+	0.0636419i
$222$		0			0
$223$		−	22.1037i		−	1.48017i	−0.672511	−	0.740087i	$-0.734784\pi$
$223$		−	22.1037i		−	1.48017i	0.672511	−	0.740087i	$-0.265216\pi$
$224$		0			0
$225$	3.55323	+	3.51775i	0.236882	+	0.234517i
$226$		0			0
$227$	−5.35387	−	5.35387i	−0.355349	−	0.355349i	0.506746	−	0.862095i	$-0.330848\pi$
$227$	−5.35387	−	5.35387i	−0.355349	−	0.355349i	−0.862095	+	0.506746i	$0.830848\pi$
$228$		0			0
$229$	−18.3018	−	18.3018i	−1.20942	−	1.20942i	−0.971215	−	0.238204i	$-0.923441\pi$
$229$	−18.3018	−	18.3018i	−1.20942	−	1.20942i	−0.238204	−	0.971215i	$-0.576559\pi$
$230$		0			0
$231$			1.80067i			0.118475i
$232$		0			0
$233$	−12.0546			−0.789721			−0.394861	−	0.918741i	$-0.629207\pi$
$233$	−12.0546			−0.789721			−0.394861	+	0.918741i	$0.629207\pi$
$234$		0			0
$235$	3.85110	+	9.23182i	0.251218	+	0.602217i
$236$		0			0
$237$	5.19504	+	5.19504i	0.337454	+	0.337454i
$238$		0			0
$239$	27.9193			1.80595			0.902974	−	0.429695i	$-0.141379\pi$
$239$	27.9193			1.80595			0.902974	+	0.429695i	$0.141379\pi$
$240$		0			0
$241$	13.7118			0.883253			0.441626	−	0.897199i	$-0.354402\pi$
$241$	13.7118			0.883253			0.441626	+	0.897199i	$0.354402\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	13.4132	−	5.59540i	0.856940	−	0.357477i
$246$		0			0
$247$	−11.8889			−0.756474
$248$		0			0
$249$			9.62077i			0.609691i
$250$		0			0
$251$	9.07173	+	9.07173i	0.572602	+	0.572602i	0.932855	−	0.360252i	$-0.117309\pi$
$251$	9.07173	+	9.07173i	0.572602	+	0.572602i	−0.360252	+	0.932855i	$0.617309\pi$
$252$		0			0
$253$	12.4605	+	12.4605i	0.783388	+	0.783388i
$254$		0			0
$255$	0.208279	−	0.506420i	0.0130430	−	0.0317132i
$256$		0			0
$257$			9.23416i			0.576011i	0.957629	+	0.288006i	$0.0929922\pi$
$257$			9.23416i			0.576011i	−0.957629	+	0.288006i	$0.907008\pi$
$258$		0			0
$259$	5.99776	−	5.99776i	0.372683	−	0.372683i
$260$		0			0
$261$	−4.89882	−	4.89882i	−0.303229	−	0.303229i
$262$		0			0
$263$	18.5516			1.14394			0.571971	−	0.820274i	$-0.306179\pi$
$263$	18.5516			1.14394			0.571971	+	0.820274i	$0.306179\pi$
$264$		0			0
$265$	−1.76846	+	4.29992i	−0.108636	+	0.264142i
$266$		0			0
$267$	−2.17423	+	2.17423i	−0.133061	+	0.133061i
$268$		0			0
$269$	14.3977	−	14.3977i	0.877844	−	0.877844i	−0.115467	−	0.993311i	$-0.536837\pi$
$269$	14.3977	−	14.3977i	0.877844	−	0.877844i	0.993311	+	0.115467i	$0.0368366\pi$
$270$		0			0
$271$	−19.2974			−1.17224			−0.586118	−	0.810226i	$-0.699344\pi$
$271$	−19.2974			−1.17224			−0.586118	+	0.810226i	$0.699344\pi$
$272$		0			0
$273$		−	3.86507i		−	0.233924i
$274$		0			0
$275$	−12.7272	+	0.0638476i	−0.767482	+	0.00385016i
$276$		0			0
$277$	3.52269	−	3.52269i	0.211658	−	0.211658i	−0.593314	−	0.804971i	$-0.702181\pi$
$277$	3.52269	−	3.52269i	0.211658	−	0.211658i	0.804971	+	0.593314i	$0.202181\pi$
$278$		0			0
$279$		−	7.60734i		−	0.455439i
$280$		0			0
$281$		−	29.2076i		−	1.74238i	−0.490945	−	0.871191i	$-0.663348\pi$
$281$		−	29.2076i		−	1.74238i	0.490945	−	0.871191i	$-0.336652\pi$
$282$		0			0
$283$	9.84279	−	9.84279i	0.585093	−	0.585093i	−0.351205	−	0.936298i	$-0.614228\pi$
$283$	9.84279	−	9.84279i	0.585093	−	0.585093i	0.936298	+	0.351205i	$0.114228\pi$
$284$		0			0
$285$	4.49052	−	1.87325i	0.265996	−	0.110961i
$286$		0			0
$287$			1.50052i			0.0885726i
$288$		0			0
$289$	16.9400			0.996472
$290$		0			0
$291$	−0.989400	+	0.989400i	−0.0579997	+	0.0579997i
$292$		0			0
$293$	11.8238	−	11.8238i	0.690755	−	0.690755i	−0.271643	−	0.962398i	$-0.587567\pi$
$293$	11.8238	−	11.8238i	0.690755	−	0.690755i	0.962398	+	0.271643i	$0.0875671\pi$
$294$		0			0
$295$	17.1416	+	7.04998i	0.998025	+	0.410466i
$296$		0			0
$297$	2.54548			0.147704
$298$		0			0
$299$	−26.7461	−	26.7461i	−1.54677	−	1.54677i
$300$		0			0
$301$	−0.484219	+	0.484219i	−0.0279099	+	0.0279099i
$302$		0			0
$303$			16.6759i			0.958004i
$304$		0			0
$305$	−0.0646434	+	0.157177i	−0.00370147	+	0.00899992i
$306$		0			0
$307$	−16.6232	−	16.6232i	−0.948733	−	0.948733i	0.0500151	−	0.998748i	$-0.484073\pi$
$307$	−16.6232	−	16.6232i	−0.948733	−	0.948733i	−0.998748	+	0.0500151i	$0.984073\pi$
$308$		0			0
$309$	−1.62097	−	1.62097i	−0.0922139	−	0.0922139i
$310$		0			0
$311$			13.8069i			0.782920i	0.920195	+	0.391460i	$0.128030\pi$
$311$			13.8069i			0.782920i	−0.920195	+	0.391460i	$0.871970\pi$
$312$		0			0
$313$	−7.40380			−0.418488			−0.209244	−	0.977864i	$-0.567100\pi$
$313$	−7.40380			−0.418488			−0.209244	+	0.977864i	$0.567100\pi$
$314$		0			0
$315$	0.608988	+	1.45986i	0.0343126	+	0.0822538i
$316$		0			0
$317$	1.80712	+	1.80712i	0.101498	+	0.101498i	0.756032	−	0.654534i	$-0.227135\pi$
$317$	1.80712	+	1.80712i	0.101498	+	0.101498i	−0.654534	+	0.756032i	$0.727135\pi$
$318$		0			0
$319$	17.6350			0.987372
$320$		0			0
$321$	−13.4210			−0.749088
$322$		0			0
$323$	−0.376786	−	0.376786i	−0.0209650	−	0.0209650i
$324$		0			0
$325$	27.3186	−	0.137046i	1.51536	−	0.00760197i
$326$		0			0
$327$	16.8373			0.931106
$328$		0			0
$329$			3.16449i			0.174464i
$330$		0			0
$331$	5.82711	+	5.82711i	0.320287	+	0.320287i	0.848877	−	0.528590i	$-0.177279\pi$
$331$	5.82711	+	5.82711i	0.320287	+	0.320287i	−0.528590	+	0.848877i	$0.677279\pi$
$332$		0			0
$333$	−8.47863	−	8.47863i	−0.464626	−	0.464626i
$334$		0			0
$335$	−22.9741	−	9.44875i	−1.25521	−	0.516240i
$336$		0			0
$337$			25.5357i			1.39102i	0.718516	+	0.695510i	$0.244822\pi$
$337$			25.5357i			1.39102i	−0.718516	+	0.695510i	$0.755178\pi$
$338$		0			0
$339$	5.60598	−	5.60598i	0.304475	−	0.304475i
$340$		0			0
$341$	13.6927	+	13.6927i	0.741499	+	0.741499i
$342$		0			0
$343$	9.54958			0.515629
$344$		0			0
$345$	14.3163	+	5.88799i	0.770766	+	0.316999i
$346$		0			0
$347$	−17.6028	+	17.6028i	−0.944970	+	0.944970i	−0.998563	−	0.0535933i	$-0.982933\pi$
$347$	−17.6028	+	17.6028i	−0.944970	+	0.944970i	0.0535933	+	0.998563i	$0.482933\pi$
$348$		0			0
$349$	−5.07562	+	5.07562i	−0.271692	+	0.271692i	−0.829781	−	0.558089i	$-0.811535\pi$
$349$	−5.07562	+	5.07562i	−0.271692	+	0.271692i	0.558089	+	0.829781i	$0.311535\pi$
$350$		0			0
$351$	−5.46378			−0.291635
$352$		0			0
$353$			0.171535i			0.00912990i	0.999990	+	0.00456495i	$0.00145307\pi$
$353$			0.171535i			0.00912990i	−0.999990	+	0.00456495i	$0.998547\pi$
$354$		0			0
$355$	1.79576	+	4.30479i	0.0953093	+	0.228474i
$356$		0			0
$357$	0.122492	−	0.122492i	0.00648299	−	0.00648299i
$358$		0			0
$359$		−	17.1694i		−	0.906169i	−0.891468	−	0.453084i	$-0.850324\pi$
$359$		−	17.1694i		−	0.906169i	0.891468	−	0.453084i	$-0.149676\pi$
$360$		0			0
$361$			14.2652i			0.750802i
$362$		0			0
$363$	3.19649	−	3.19649i	0.167772	−	0.167772i
$364$		0			0
$365$	−20.0169	+	8.35016i	−1.04773	+	0.437068i
$366$		0			0
$367$			23.3124i			1.21690i	0.793593	+	0.608450i	$0.208208\pi$
$367$			23.3124i			1.21690i	−0.793593	+	0.608450i	$0.791792\pi$
$368$		0			0
$369$	2.12118			0.110424
$370$		0			0
$371$	−1.04006	+	1.04006i	−0.0539973	+	0.0539973i
$372$		0			0
$373$	1.11817	−	1.11817i	0.0578964	−	0.0578964i	−0.677566	−	0.735462i	$-0.736965\pi$
$373$	1.11817	−	1.11817i	0.0578964	−	0.0578964i	0.735462	+	0.677566i	$0.236965\pi$
$374$		0			0
$375$	−10.2968	+	4.35614i	−0.531724	+	0.224950i
$376$		0			0
$377$	−37.8529			−1.94953
$378$		0			0
$379$	−22.3707	−	22.3707i	−1.14910	−	1.14910i	−0.986729	−	0.162375i	$-0.948085\pi$
$379$	−22.3707	−	22.3707i	−1.14910	−	1.14910i	−0.162375	−	0.986729i	$-0.551915\pi$
$380$		0			0
$381$	−13.7509	+	13.7509i	−0.704478	+	0.704478i
$382$		0			0
$383$			32.1168i			1.64109i	0.571579	+	0.820547i	$0.306331\pi$
$383$			32.1168i			1.64109i	−0.571579	+	0.820547i	$0.693669\pi$
$384$		0			0
$385$	−3.72378	−	1.53151i	−0.189781	−	0.0780528i
$386$		0			0
$387$	0.684507	+	0.684507i	0.0347955	+	0.0347955i
$388$		0			0
$389$	−22.7409	−	22.7409i	−1.15301	−	1.15301i	−0.985946	−	0.167062i	$-0.946572\pi$
$389$	−22.7409	−	22.7409i	−1.15301	−	1.15301i	−0.167062	−	0.985946i	$-0.553428\pi$
$390$		0			0
$391$		−	1.69529i		−	0.0857342i
$392$		0			0
$393$	0.500701			0.0252570
$394$		0			0
$395$	−15.1618	+	6.32484i	−0.762874	+	0.318237i
$396$		0			0
$397$	−21.6530	−	21.6530i	−1.08673	−	1.08673i	−0.995863	−	0.0908707i	$-0.971035\pi$
$397$	−21.6530	−	21.6530i	−1.08673	−	1.08673i	−0.0908707	−	0.995863i	$-0.528965\pi$
$398$		0			0
$399$	1.53926			0.0770596
$400$		0			0
$401$	17.1600			0.856931			0.428466	−	0.903558i	$-0.359054\pi$
$401$	17.1600			0.856931			0.428466	+	0.903558i	$0.359054\pi$
$402$		0			0
$403$	−29.3908	−	29.3908i	−1.46406	−	1.46406i
$404$		0			0
$405$	2.06370	−	0.860885i	0.102546	−	0.0427777i
$406$		0			0
$407$	30.5218			1.51291
$408$		0			0
$409$			17.9588i			0.888006i	0.896025	+	0.444003i	$0.146442\pi$
$409$			17.9588i			0.888006i	−0.896025	+	0.444003i	$0.853558\pi$
$410$		0			0
$411$	−5.16211	−	5.16211i	−0.254628	−	0.254628i
$412$		0			0
$413$	4.14621	+	4.14621i	0.204022	+	0.204022i
$414$		0			0
$415$	−19.8957	−	8.18267i	−0.976642	−	0.401671i
$416$		0			0
$417$			12.5231i			0.613260i
$418$		0			0
$419$	−23.4031	+	23.4031i	−1.14332	+	1.14332i	−0.155476	+	0.987840i	$0.549691\pi$
$419$	−23.4031	+	23.4031i	−1.14332	+	1.14332i	−0.987840	+	0.155476i	$0.950309\pi$
$420$		0			0
$421$	−27.0016	−	27.0016i	−1.31598	−	1.31598i	−0.916932	−	0.399043i	$-0.869342\pi$
$421$	−27.0016	−	27.0016i	−1.31598	−	1.31598i	−0.399043	−	0.916932i	$-0.630658\pi$
$422$		0			0
$423$	4.47342			0.217505
$424$		0			0
$425$	0.870129	+	0.861442i	0.0422075	+	0.0417861i
$426$		0			0
$427$	−0.0380178	+	0.0380178i	−0.00183981	+	0.00183981i
$428$		0			0
$429$	9.83441	−	9.83441i	0.474810	−	0.474810i
$430$		0			0
$431$	28.4043			1.36819			0.684093	−	0.729395i	$-0.260198\pi$
$431$	28.4043			1.36819			0.684093	+	0.729395i	$0.260198\pi$
$432$		0			0
$433$		−	4.04564i		−	0.194421i	−0.995264	−	0.0972106i	$-0.969008\pi$
$433$		−	4.04564i		−	0.194421i	0.995264	−	0.0972106i	$-0.0309920\pi$
$434$		0			0
$435$	14.2973	−	5.96419i	0.685503	−	0.285961i
$436$		0			0
$437$	10.6516	−	10.6516i	0.509537	−	0.509537i
$438$		0			0
$439$			10.4690i			0.499660i	0.968290	+	0.249830i	$0.0803748\pi$
$439$			10.4690i			0.499660i	−0.968290	+	0.249830i	$0.919625\pi$
$440$		0			0
$441$		−	6.49959i		−	0.309504i
$442$		0			0
$443$	1.81582	−	1.81582i	0.0862722	−	0.0862722i	−0.662654	−	0.748926i	$-0.730570\pi$
$443$	1.81582	−	1.81582i	0.0862722	−	0.0862722i	0.748926	+	0.662654i	$0.230570\pi$
$444$		0			0
$445$	−2.64707	−	6.34554i	−0.125483	−	0.300807i
$446$		0			0
$447$			7.65634i			0.362132i
$448$		0			0
$449$	−22.2064			−1.04799			−0.523993	−	0.851723i	$-0.675558\pi$
$449$	−22.2064			−1.04799			−0.523993	+	0.851723i	$0.675558\pi$
$450$		0			0
$451$	−3.81797	+	3.81797i	−0.179781	+	0.179781i
$452$		0			0
$453$	0.241511	−	0.241511i	0.0113472	−	0.0113472i
$454$		0			0
$455$	7.99294	+	3.28732i	0.374715	+	0.154112i
$456$		0			0
$457$	12.2280			0.572000			0.286000	−	0.958230i	$-0.407674\pi$
$457$	12.2280			0.572000			0.286000	+	0.958230i	$0.407674\pi$
$458$		0			0
$459$	−0.173159	−	0.173159i	−0.00808238	−	0.00808238i
$460$		0			0
$461$	0.723447	−	0.723447i	0.0336943	−	0.0336943i	−0.690059	−	0.723753i	$-0.742415\pi$
$461$	0.723447	−	0.723447i	0.0336943	−	0.0336943i	0.723753	+	0.690059i	$0.242415\pi$
$462$		0			0
$463$			5.42343i			0.252048i	0.992027	+	0.126024i	$0.0402217\pi$
$463$			5.42343i			0.252048i	−0.992027	+	0.126024i	$0.959778\pi$
$464$		0			0
$465$	15.7320	+	6.47021i	0.729552	+	0.300049i
$466$		0			0
$467$	13.3242	+	13.3242i	0.616571	+	0.616571i	0.944650	−	0.328079i	$-0.106401\pi$
$467$	13.3242	+	13.3242i	0.616571	+	0.616571i	−0.328079	+	0.944650i	$0.606401\pi$
$468$		0			0
$469$	−5.55696	−	5.55696i	−0.256597	−	0.256597i
$470$		0			0
$471$		−	4.05122i		−	0.186671i
$472$		0			0
$473$	−2.46413			−0.113301
$474$		0			0
$475$	0.0545788	+	10.8796i	0.00250425	+	0.499191i
$476$		0			0
$477$	1.47026	+	1.47026i	0.0673188	+	0.0673188i
$478$		0			0
$479$	1.25963			0.0575541			0.0287771	−	0.999586i	$-0.490839\pi$
$479$	1.25963			0.0575541			0.0287771	+	0.999586i	$0.490839\pi$
$480$		0			0
$481$	−65.5140			−2.98718
$482$		0			0
$483$	3.46282	+	3.46282i	0.157564	+	0.157564i
$484$		0			0
$485$	−1.20457	−	2.88758i	−0.0546967	−	0.131118i
$486$		0			0
$487$	−15.8116			−0.716491			−0.358246	−	0.933627i	$-0.616625\pi$
$487$	−15.8116			−0.716491			−0.358246	+	0.933627i	$0.616625\pi$
$488$		0			0
$489$			8.40349i			0.380019i
$490$		0			0
$491$	15.6008	+	15.6008i	0.704054	+	0.704054i	0.965278	−	0.261224i	$-0.0841263\pi$
$491$	15.6008	+	15.6008i	0.704054	+	0.704054i	−0.261224	+	0.965278i	$0.584126\pi$
$492$		0			0
$493$	−1.19964	−	1.19964i	−0.0540292	−	0.0540292i
$494$		0			0
$495$	−2.16499	+	5.26405i	−0.0973090	+	0.236601i
$496$		0			0
$497$			1.47560i			0.0661896i
$498$		0			0
$499$	−25.6650	+	25.6650i	−1.14892	+	1.14892i	−0.162159	+	0.986765i	$0.551846\pi$
$499$	−25.6650	+	25.6650i	−1.14892	+	1.14892i	−0.986765	+	0.162159i	$0.948154\pi$
$500$		0			0
$501$	−10.2244	−	10.2244i	−0.456792	−	0.456792i
$502$		0			0
$503$	−4.72004			−0.210456			−0.105228	−	0.994448i	$-0.533557\pi$
$503$	−4.72004			−0.210456			−0.105228	+	0.994448i	$0.533557\pi$
$504$		0			0
$505$	−34.4857	−	14.1832i	−1.53459	−	0.631144i
$506$		0			0
$507$	−11.9168	+	11.9168i	−0.529244	+	0.529244i
$508$		0			0
$509$	−11.8862	+	11.8862i	−0.526848	+	0.526848i	−0.919631	−	0.392783i	$-0.871512\pi$
$509$	−11.8862	+	11.8862i	−0.526848	+	0.526848i	0.392783	+	0.919631i	$0.371512\pi$
$510$		0			0
$511$	−6.86141			−0.303531
$512$		0			0
$513$		−	2.17595i		−	0.0960706i
$514$		0			0
$515$	4.73084	−	1.97349i	0.208466	−	0.0869625i
$516$		0			0
$517$	−8.05183	+	8.05183i	−0.354119	+	0.354119i
$518$		0			0
$519$		−	9.40587i		−	0.412872i
$520$		0			0
$521$			5.01467i			0.219696i	0.993948	+	0.109848i	$0.0350365\pi$
$521$			5.01467i			0.219696i	−0.993948	+	0.109848i	$0.964964\pi$
$522$		0			0
$523$	−18.9502	+	18.9502i	−0.828635	+	0.828635i	−0.987328	−	0.158693i	$-0.949272\pi$
$523$	−18.9502	+	18.9502i	−0.828635	+	0.828635i	0.158693	+	0.987328i	$0.449272\pi$
$524$		0			0
$525$	−3.53694	+	0.0177435i	−0.154365	+	0.000774388i
$526$		0			0
$527$		−	1.86292i		−	0.0811499i
$528$		0			0
$529$	24.9252			1.08370
$530$		0			0
$531$	5.86121	−	5.86121i	0.254355	−	0.254355i
$532$		0			0
$533$	8.19512	−	8.19512i	0.354970	−	0.354970i
$534$		0			0
$535$	11.4149	−	27.7546i	0.493508	−	1.19994i
$536$		0			0
$537$	−24.4178			−1.05370
$538$		0			0
$539$	11.6988	+	11.6988i	0.503903	+	0.503903i
$540$		0			0
$541$	−22.8366	+	22.8366i	−0.981822	+	0.981822i	−0.999838	−	0.0180153i	$-0.994265\pi$
$541$	−22.8366	+	22.8366i	−0.981822	+	0.981822i	0.0180153	+	0.999838i	$0.494265\pi$
$542$		0			0
$543$			7.24419i			0.310878i
$544$		0			0
$545$	−14.3205	+	34.8195i	−0.613423	+	1.49150i
$546$		0			0
$547$	0.00963023	+	0.00963023i	0.000411759	+	0.000411759i	0.707313	−	0.706901i	$-0.249907\pi$
$547$	0.00963023	+	0.00963023i	0.000411759	+	0.000411759i	−0.706901	+	0.707313i	$0.749907\pi$
$548$		0			0
$549$	0.0537432	+	0.0537432i	0.00229371	+	0.00229371i
$550$		0			0
$551$		−	15.0749i		−	0.642214i
$552$		0			0
$553$	−5.19718			−0.221006
$554$		0			0
$555$	24.7450	−	10.3225i	1.05037	−	0.438167i
$556$		0			0
$557$	25.6660	+	25.6660i	1.08750	+	1.08750i	0.995785	+	0.0917192i	$0.0292362\pi$
$557$	25.6660	+	25.6660i	1.08750	+	1.08750i	0.0917192	+	0.995785i	$0.470764\pi$
$558$		0			0
$559$	5.28916			0.223707
$560$		0			0
$561$	0.623348			0.0263178
$562$		0			0
$563$	6.16719	+	6.16719i	0.259916	+	0.259916i	0.825020	−	0.565104i	$-0.191164\pi$
$563$	6.16719	+	6.16719i	0.259916	+	0.259916i	−0.565104	+	0.825020i	$0.691164\pi$
$564$		0			0
$565$	6.82515	+	16.3612i	0.287136	+	0.688319i
$566$		0			0
$567$	0.707398			0.0297079
$568$		0			0
$569$			4.05892i			0.170159i	0.996374	+	0.0850794i	$0.0271144\pi$
$569$			4.05892i			0.170159i	−0.996374	+	0.0850794i	$0.972886\pi$
$570$		0			0
$571$	12.9113	+	12.9113i	0.540323	+	0.540323i	0.923624	−	0.383301i	$-0.125213\pi$
$571$	12.9113	+	12.9113i	0.540323	+	0.540323i	−0.383301	+	0.923624i	$0.625213\pi$
$572$		0			0
$573$	12.5893	+	12.5893i	0.525925	+	0.525925i
$574$		0			0
$575$	−24.3527	+	24.5983i	−1.01558	+	1.02582i
$576$		0			0
$577$		−	10.4193i		−	0.433761i	−0.976198	−	0.216880i	$-0.930412\pi$
$577$		−	10.4193i		−	0.433761i	0.976198	−	0.216880i	$-0.0695882\pi$
$578$		0			0
$579$	−12.1780	+	12.1780i	−0.506099	+	0.506099i
$580$		0			0
$581$	−4.81236	−	4.81236i	−0.199650	−	0.199650i
$582$		0			0
$583$	−5.29274			−0.219203
$584$		0			0
$585$	4.64706	−	11.2991i	0.192132	−	0.467160i
$586$		0			0
$587$	27.7728	−	27.7728i	1.14631	−	1.14631i	0.159033	−	0.987273i	$-0.449162\pi$
$587$	27.7728	−	27.7728i	1.14631	−	1.14631i	0.987273	−	0.159033i	$-0.0508376\pi$
$588$		0			0
$589$	11.7049	−	11.7049i	0.482291	−	0.482291i
$590$		0			0
$591$	−14.2502			−0.586175
$592$		0			0
$593$			25.4466i			1.04496i	0.852650	+	0.522482i	$0.174994\pi$
$593$			25.4466i			1.04496i	−0.852650	+	0.522482i	$0.825006\pi$
$594$		0			0
$595$	0.149132	+	0.357497i	0.00611380	+	0.0146559i
$596$		0			0
$597$	4.06006	−	4.06006i	0.166167	−	0.166167i
$598$		0			0
$599$			1.32051i			0.0539544i	0.999636	+	0.0269772i	$0.00858816\pi$
$599$			1.32051i			0.0539544i	−0.999636	+	0.0269772i	$0.991412\pi$
$600$		0			0
$601$		−	23.8236i		−	0.971787i	−0.874018	−	0.485893i	$-0.838494\pi$
$601$		−	23.8236i		−	0.971787i	0.874018	−	0.485893i	$-0.161506\pi$
$602$		0			0
$603$	−7.85550	+	7.85550i	−0.319901	+	0.319901i
$604$		0			0
$605$	3.89165	+	9.32902i	0.158218	+	0.379279i
$606$		0			0
$607$			1.20300i			0.0488283i	0.999702	+	0.0244141i	$0.00777203\pi$
$607$			1.20300i			0.0488283i	−0.999702	+	0.0244141i	$0.992228\pi$
$608$		0			0
$609$	4.90083			0.198592
$610$		0			0
$611$	17.2830	−	17.2830i	0.699193	−	0.699193i
$612$		0			0
$613$	−4.84340	+	4.84340i	−0.195623	+	0.195623i	−0.798121	−	0.602498i	$-0.794172\pi$
$613$	−4.84340	+	4.84340i	−0.195623	+	0.195623i	0.602498	+	0.798121i	$0.294172\pi$
$614$		0			0
$615$	−1.80411	+	4.38659i	−0.0727486	+	0.176884i
$616$		0			0
$617$	26.9719			1.08585			0.542924	−	0.839782i	$-0.317317\pi$
$617$	26.9719			1.08585			0.542924	+	0.839782i	$0.317317\pi$
$618$		0			0
$619$	−19.9202	−	19.9202i	−0.800660	−	0.800660i	0.182539	−	0.983199i	$-0.441568\pi$
$619$	−19.9202	−	19.9202i	−0.800660	−	0.800660i	−0.983199	+	0.182539i	$0.941568\pi$
$620$		0			0
$621$	4.89516	−	4.89516i	0.196436	−	0.196436i
$622$		0			0
$623$		−	2.17513i		−	0.0871446i
$624$		0			0
$625$	−0.250824	−	24.9987i	−0.0100330	−	0.999950i
$626$		0			0
$627$	3.91656	+	3.91656i	0.156412	+	0.156412i
$628$		0			0
$629$	−2.07628	−	2.07628i	−0.0827868	−	0.0827868i
$630$		0			0
$631$		−	12.7975i		−	0.509462i	−0.967012	−	0.254731i	$-0.918013\pi$
$631$		−	12.7975i		−	0.509462i	0.967012	−	0.254731i	$-0.0819870\pi$
$632$		0			0
$633$	13.7648			0.547101
$634$		0			0
$635$	−16.7413	−	40.1321i	−0.664360	−	1.59260i
$636$		0			0
$637$	−25.1110	−	25.1110i	−0.994934	−	0.994934i
$638$		0			0
$639$	2.08595			0.0825190
$640$		0			0
$641$	10.9406			0.432129			0.216064	−	0.976379i	$-0.430678\pi$
$641$	10.9406			0.432129			0.216064	+	0.976379i	$0.430678\pi$
$642$		0			0
$643$	−18.2613	−	18.2613i	−0.720157	−	0.720157i	0.248480	−	0.968637i	$-0.420069\pi$
$643$	−18.2613	−	18.2613i	−0.720157	−	0.720157i	−0.968637	+	0.248480i	$0.920069\pi$
$644$		0			0
$645$	−1.99775	+	0.833371i	−0.0786612	+	0.0328140i
$646$		0			0
$647$	−10.5055			−0.413014			−0.206507	−	0.978445i	$-0.566210\pi$
$647$	−10.5055			−0.413014			−0.206507	+	0.978445i	$0.566210\pi$
$648$		0			0
$649$			21.0995i			0.828228i
$650$		0			0
$651$	3.80523	+	3.80523i	0.149139	+	0.149139i
$652$		0			0
$653$	−11.1836	−	11.1836i	−0.437648	−	0.437648i	0.453572	−	0.891220i	$-0.350150\pi$
$653$	−11.1836	−	11.1836i	−0.437648	−	0.437648i	−0.891220	+	0.453572i	$0.850150\pi$
$654$		0			0
$655$	−0.425857	+	1.03545i	−0.0166396	+	0.0404583i
$656$		0			0
$657$			9.69951i			0.378414i
$658$		0			0
$659$	−2.60687	+	2.60687i	−0.101549	+	0.101549i	−0.756056	−	0.654507i	$-0.772876\pi$
$659$	−2.60687	+	2.60687i	−0.101549	+	0.101549i	0.654507	+	0.756056i	$0.272876\pi$
$660$		0			0
$661$	15.9084	+	15.9084i	0.618766	+	0.618766i	0.945215	−	0.326449i	$-0.105852\pi$
$661$	15.9084	+	15.9084i	0.618766	+	0.618766i	−0.326449	+	0.945215i	$0.605852\pi$
$662$		0			0
$663$	−1.33799			−0.0519634
$664$		0			0
$665$	−1.30918	+	3.18319i	−0.0507677	+	0.123439i
$666$		0			0
$667$	33.9135	−	33.9135i	1.31314	−	1.31314i
$668$		0			0
$669$	15.6297	−	15.6297i	0.604278	−	0.604278i
$670$		0			0
$671$	−0.193468			−0.00746874
$672$		0			0
$673$		−	27.1091i		−	1.04498i	−0.852645	−	0.522490i	$-0.825003\pi$
$673$		−	27.1091i		−	1.04498i	0.852645	−	0.522490i	$-0.174997\pi$
$674$		0			0
$675$	0.0250827	+	4.99994i	0.000965434	+	0.192448i
$676$		0			0
$677$	11.0637	−	11.0637i	0.425211	−	0.425211i	−0.461782	−	0.886993i	$-0.652790\pi$
$677$	11.0637	−	11.0637i	0.425211	−	0.425211i	0.886993	+	0.461782i	$0.152790\pi$
$678$		0			0
$679$		−	0.989807i		−	0.0379853i
$680$		0			0
$681$		−	7.57152i		−	0.290141i
$682$		0			0
$683$	−17.4289	+	17.4289i	−0.666898	+	0.666898i	−0.956997	−	0.290098i	$-0.906312\pi$
$683$	−17.4289	+	17.4289i	−0.666898	+	0.666898i	0.290098	+	0.956997i	$0.406312\pi$
$684$		0			0
$685$	15.0657	−	6.28474i	0.575631	−	0.240128i
$686$		0			0
$687$		−	25.8827i		−	0.987487i
$688$		0			0
$689$	11.3607			0.432807
$690$		0			0
$691$	−26.0352	+	26.0352i	−0.990426	+	0.990426i	−0.999955	−	0.00952887i	$-0.996967\pi$
$691$	−26.0352	+	26.0352i	−0.990426	+	0.990426i	0.00952887	+	0.999955i	$0.496967\pi$
$692$		0			0
$693$	−1.27326	+	1.27326i	−0.0483673	+	0.0483673i
$694$		0			0
$695$	−25.8978	−	10.6512i	−0.982359	−	0.404023i
$696$		0			0
$697$	0.519443			0.0196753
$698$		0			0
$699$	−8.52387	−	8.52387i	−0.322402	−	0.322402i
$700$		0			0
$701$	2.08057	−	2.08057i	0.0785822	−	0.0785822i	−0.666723	−	0.745305i	$-0.732304\pi$
$701$	2.08057	−	2.08057i	0.0785822	−	0.0785822i	0.745305	+	0.666723i	$0.232304\pi$
$702$		0			0
$703$		−	26.0910i		−	0.984039i
$704$		0			0
$705$	−3.80474	+	9.25102i	−0.143295	+	0.348414i
$706$		0			0
$707$	−8.34137	−	8.34137i	−0.313709	−	0.313709i
$708$		0			0
$709$	−3.27484	−	3.27484i	−0.122989	−	0.122989i	0.642933	−	0.765922i	$-0.277717\pi$
$709$	−3.27484	−	3.27484i	−0.122989	−	0.122989i	−0.765922	+	0.642933i	$0.777717\pi$
$710$		0			0
$711$			7.34690i			0.275530i
$712$		0			0
$713$	52.6641			1.97229
$714$		0			0
$715$	11.9732	+	28.7019i	0.447771	+	1.07339i
$716$		0			0
$717$	19.7419	+	19.7419i	0.737275	+	0.737275i
$718$		0			0
$719$	2.03220			0.0757882			0.0378941	−	0.999282i	$-0.487935\pi$
$719$	2.03220			0.0757882			0.0378941	+	0.999282i	$0.487935\pi$
$720$		0			0
$721$	1.62164			0.0603930
$722$		0			0
$723$	9.69568	+	9.69568i	0.360586	+	0.360586i
$724$		0			0
$725$	0.173772	+	34.6394i	0.00645375	+	1.28648i
$726$		0			0
$727$	6.37077			0.236279			0.118139	−	0.992997i	$-0.462307\pi$
$727$	6.37077			0.236279			0.118139	+	0.992997i	$0.462307\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	0.167625	+	0.167625i	0.00619984	+	0.00619984i
$732$		0			0
$733$	6.95026	+	6.95026i	0.256714	+	0.256714i	0.823716	−	0.567002i	$-0.191897\pi$
$733$	6.95026	+	6.95026i	0.256714	+	0.256714i	−0.567002	+	0.823716i	$0.691897\pi$
$734$		0			0
$735$	13.4411	+	5.52804i	0.495784	+	0.203905i
$736$		0			0
$737$		−	28.2787i		−	1.04166i
$738$		0			0
$739$	−0.0483355	+	0.0483355i	−0.00177805	+	0.00177805i	−0.707995	−	0.706217i	$-0.750400\pi$
$739$	−0.0483355	+	0.0483355i	−0.00177805	+	0.00177805i	0.706217	+	0.707995i	$0.250400\pi$
$740$		0			0
$741$	−8.40674	−	8.40674i	−0.308829	−	0.308829i
$742$		0			0
$743$	−0.148848			−0.00546069			−0.00273035	−	0.999996i	$-0.500869\pi$
$743$	−0.148848			−0.00546069			−0.00273035	+	0.999996i	$0.500869\pi$
$744$		0			0
$745$	−15.8333	−	6.51188i	−0.580087	−	0.238577i
$746$		0			0
$747$	−6.80291	+	6.80291i	−0.248905	+	0.248905i
$748$		0			0
$749$	6.71327	−	6.71327i	0.245297	−	0.245297i
$750$		0			0
$751$	−1.69304			−0.0617798			−0.0308899	−	0.999523i	$-0.509834\pi$
$751$	−1.69304			−0.0617798			−0.0308899	+	0.999523i	$0.509834\pi$
$752$		0			0
$753$			12.8294i			0.467528i
$754$		0			0
$755$	0.294034	+	0.704855i	0.0107010	+	0.0256523i
$756$		0			0
$757$	26.6876	−	26.6876i	0.969977	−	0.969977i	−0.0295851	−	0.999562i	$-0.509419\pi$
$757$	26.6876	−	26.6876i	0.969977	−	0.969977i	0.999562	+	0.0295851i	$0.00941860\pi$
$758$		0			0
$759$			17.6219i			0.639633i
$760$		0			0
$761$			17.1363i			0.621189i	0.950542	+	0.310595i	$0.100528\pi$
$761$			17.1363i			0.621189i	−0.950542	+	0.310595i	$0.899472\pi$
$762$		0			0
$763$	−8.42212	+	8.42212i	−0.304901	+	0.304901i
$764$		0			0
$765$	0.505369	−	0.210817i	0.0182716	−	0.00762211i
$766$		0			0
$767$		−	45.2893i		−	1.63530i
$768$		0			0
$769$	−25.6406			−0.924622			−0.462311	−	0.886718i	$-0.652980\pi$
$769$	−25.6406			−0.924622			−0.462311	+	0.886718i	$0.652980\pi$
$770$		0			0
$771$	−6.52954	+	6.52954i	−0.235156	+	0.235156i
$772$		0			0
$773$	−27.4452	+	27.4452i	−0.987137	+	0.987137i	−0.999918	−	0.0127818i	$-0.995931\pi$
$773$	−27.4452	+	27.4452i	−0.987137	+	0.987137i	0.0127818	+	0.999918i	$0.495931\pi$
$774$		0			0
$775$	−26.7607	+	27.0306i	−0.961274	+	0.970967i
$776$		0			0
$777$	8.48212			0.304294
$778$		0			0
$779$	3.26371	+	3.26371i	0.116934	+	0.116934i
$780$		0			0
$781$	−3.75456	+	3.75456i	−0.134349	+	0.134349i
$782$		0			0
$783$		−	6.92797i		−	0.247586i
$784$		0			0
$785$	8.37792	+	3.44565i	0.299021	+	0.122981i
$786$		0			0
$787$	−9.65912	−	9.65912i	−0.344310	−	0.344310i	0.513675	−	0.857985i	$-0.328284\pi$
$787$	−9.65912	−	9.65912i	−0.344310	−	0.344310i	−0.857985	+	0.513675i	$0.828284\pi$
$788$		0			0
$789$	13.1180	+	13.1180i	0.467012	+	0.467012i
$790$		0			0
$791$			5.60829i			0.199408i
$792$		0			0
$793$	0.415271			0.0147467
$794$		0			0
$795$	−4.29099	+	1.79001i	−0.152186	+	0.0634851i
$796$		0			0
$797$	11.9978	+	11.9978i	0.424984	+	0.424984i	0.886916	−	0.461931i	$-0.152843\pi$
$797$	11.9978	+	11.9978i	0.424984	+	0.424984i	−0.461931	+	0.886916i	$0.652843\pi$
$798$		0			0
$799$	1.09547			0.0387549
$800$		0			0
$801$	−3.07483			−0.108644
$802$		0			0
$803$	−17.4584	−	17.4584i	−0.616094	−	0.616094i
$804$		0			0
$805$	−10.1063	+	4.21590i	−0.356201	+	0.148591i
$806$		0			0
$807$	20.3614			0.716756
$808$		0			0
$809$			36.2916i			1.27594i	0.770060	+	0.637972i	$0.220226\pi$
$809$			36.2916i			1.27594i	−0.770060	+	0.637972i	$0.779774\pi$
$810$		0			0
$811$	−17.0781	−	17.0781i	−0.599693	−	0.599693i	0.340538	−	0.940231i	$-0.389391\pi$
$811$	−17.0781	−	17.0781i	−0.599693	−	0.599693i	−0.940231	+	0.340538i	$0.889391\pi$
$812$		0			0
$813$	−13.6453	−	13.6453i	−0.478563	−	0.478563i
$814$		0			0
$815$	−17.3784	−	7.14735i	−0.608738	−	0.250361i
$816$		0			0
$817$			2.10641i			0.0736939i
$818$		0			0
$819$	2.73301	−	2.73301i	0.0954992	−	0.0954992i
$820$		0			0
$821$	21.9249	+	21.9249i	0.765183	+	0.765183i	0.977254	−	0.212071i	$-0.0680209\pi$
$821$	21.9249	+	21.9249i	0.765183	+	0.765183i	−0.212071	+	0.977254i	$0.568021\pi$
$822$		0			0
$823$	4.38382			0.152810			0.0764052	−	0.997077i	$-0.475656\pi$
$823$	4.38382			0.152810			0.0764052	+	0.997077i	$0.475656\pi$
$824$		0			0
$825$	−9.04467	−	8.95438i	−0.314895	−	0.311751i
$826$		0			0
$827$	−21.5889	+	21.5889i	−0.750718	+	0.750718i	−0.974613	−	0.223895i	$-0.928123\pi$
$827$	−21.5889	+	21.5889i	−0.750718	+	0.750718i	0.223895	+	0.974613i	$0.428123\pi$
$828$		0			0
$829$	7.88066	−	7.88066i	0.273707	−	0.273707i	−0.556884	−	0.830590i	$-0.688003\pi$
$829$	7.88066	−	7.88066i	0.273707	−	0.273707i	0.830590	+	0.556884i	$0.188003\pi$
$830$		0			0
$831$	4.98183			0.172818
$832$		0			0
$833$		−	1.59165i		−	0.0551473i
$834$		0			0
$835$	29.8401	−	12.4480i	1.03266	−	0.430779i
$836$		0			0
$837$	5.37920	−	5.37920i	0.185932	−	0.185932i
$838$		0			0
$839$		−	6.03706i		−	0.208423i	−0.994555	−	0.104211i	$-0.966768\pi$
$839$		−	6.03706i		−	0.208423i	0.994555	−	0.104211i	$-0.0332318\pi$
$840$		0			0
$841$		−	18.9968i		−	0.655063i
$842$		0			0
$843$	20.6529	−	20.6529i	0.711324	−	0.711324i
$844$		0			0
$845$	−14.5084	−	34.7794i	−0.499105	−	1.19645i
$846$		0			0
$847$			3.19781i			0.109878i
$848$		0			0
$849$	13.9198			0.477727
$850$		0			0
$851$	58.6959	−	58.6959i	2.01207	−	2.01207i
$852$		0			0
$853$	−12.6685	+	12.6685i	−0.433763	+	0.433763i	−0.889906	−	0.456144i	$-0.849230\pi$
$853$	−12.6685	+	12.6685i	−0.433763	+	0.433763i	0.456144	+	0.889906i	$0.349230\pi$
$854$		0			0
$855$	4.49986	+	1.85069i	0.153892	+	0.0632924i
$856$		0			0
$857$	4.79580			0.163821			0.0819106	−	0.996640i	$-0.473898\pi$
$857$	4.79580			0.163821			0.0819106	+	0.996640i	$0.473898\pi$
$858$		0			0
$859$	34.0244	+	34.0244i	1.16090	+	1.16090i	0.984280	+	0.176616i	$0.0565152\pi$
$859$	34.0244	+	34.0244i	1.16090	+	1.16090i	0.176616	+	0.984280i	$0.443485\pi$
$860$		0			0
$861$	−1.06102	+	1.06102i	−0.0361596	+	0.0361596i
$862$		0			0
$863$			8.20297i			0.279232i	0.990206	+	0.139616i	$0.0445869\pi$
$863$			8.20297i			0.279232i	−0.990206	+	0.139616i	$0.955413\pi$
$864$		0			0
$865$	19.4513	+	7.99990i	0.661365	+	0.272005i
$866$		0			0
$867$	11.9784	+	11.9784i	0.406808	+	0.406808i
$868$		0			0
$869$	−13.2239	−	13.2239i	−0.448590	−	0.448590i
$870$		0			0
$871$			60.6991i			2.05671i
$872$		0			0
$873$	−1.39922			−0.0473565
$874$		0			0
$875$	2.97155	−	7.32948i	0.100457	−	0.247782i
$876$		0			0
$877$	−23.9525	−	23.9525i	−0.808817	−	0.808817i	0.175638	−	0.984455i	$-0.443801\pi$
$877$	−23.9525	−	23.9525i	−0.808817	−	0.808817i	−0.984455	+	0.175638i	$0.943801\pi$
$878$		0			0
$879$	16.7214			0.563999
$880$		0			0
$881$	27.4850			0.925993			0.462997	−	0.886360i	$-0.346774\pi$
$881$	27.4850			0.925993			0.462997	+	0.886360i	$0.346774\pi$
$882$		0			0
$883$	22.9566	+	22.9566i	0.772550	+	0.772550i	0.978552	−	0.206001i	$-0.0660452\pi$
$883$	22.9566	+	22.9566i	0.772550	+	0.772550i	−0.206001	+	0.978552i	$0.566045\pi$
$884$		0			0
$885$	7.13588	+	17.1061i	0.239870	+	0.575014i
$886$		0			0
$887$	−8.52038			−0.286086			−0.143043	−	0.989716i	$-0.545689\pi$
$887$	−8.52038			−0.286086			−0.143043	+	0.989716i	$0.545689\pi$
$888$		0			0
$889$		−	13.7565i		−	0.461379i
$890$		0			0
$891$	1.79993	+	1.79993i	0.0602998	+	0.0602998i
$892$		0			0
$893$	6.88294	+	6.88294i	0.230329	+	0.230329i
$894$		0			0
$895$	20.7678	−	50.4958i	0.694192	−	1.68789i
$896$		0			0
$897$		−	37.8247i		−	1.26293i
$898$		0			0
$899$	37.2670	−	37.2670i	1.24292	−	1.24292i
$900$		0			0
$901$	0.360044	+	0.360044i	0.0119948	+	0.0119948i
$902$		0			0
$903$	−0.684789			−0.0227883
$904$		0			0
$905$	−14.9810	−	6.16134i	−0.497984	−	0.204810i
$906$		0			0
$907$	21.1812	−	21.1812i	0.703312	−	0.703312i	−0.261808	−	0.965120i	$-0.584319\pi$
$907$	21.1812	−	21.1812i	0.703312	−	0.703312i	0.965120	+	0.261808i	$0.0843188\pi$
$908$		0			0
$909$	−11.7916	+	11.7916i	−0.391104	+	0.391104i
$910$		0			0
$911$	12.3002			0.407525			0.203763	−	0.979020i	$-0.434683\pi$
$911$	12.3002			0.407525			0.203763	+	0.979020i	$0.434683\pi$
$912$		0			0
$913$		−	24.4895i		−	0.810484i
$914$		0			0
$915$	−0.156851	+	0.0654311i	−0.00518532	+	0.00216308i
$916$		0			0
$917$	−0.250454	+	0.250454i	−0.00827070	+	0.00827070i
$918$		0			0
$919$		−	3.59430i		−	0.118565i	−0.998241	−	0.0592826i	$-0.981119\pi$
$919$		−	3.59430i		−	0.118565i	0.998241	−	0.0592826i	$-0.0188813\pi$
$920$		0			0
$921$		−	23.5087i		−	0.774638i
$922$		0			0
$923$	8.05902	−	8.05902i	0.265266	−	0.265266i
$924$		0			0
$925$	0.300757	+	59.9522i	0.00988882	+	1.97122i
$926$		0			0
$927$		−	2.29240i		−	0.0752923i
$928$		0			0
$929$	−35.8527			−1.17629			−0.588145	−	0.808756i	$-0.700142\pi$
$929$	−35.8527			−1.17629			−0.588145	+	0.808756i	$0.700142\pi$
$930$		0			0
$931$	10.0005	−	10.0005i	0.327752	−	0.327752i
$932$		0			0
$933$	−9.76298	+	9.76298i	−0.319626	+	0.319626i
$934$		0			0
$935$	−0.530171	+	1.28908i	−0.0173385	+	0.0421575i
$936$		0			0
$937$	40.7563			1.33145			0.665725	−	0.746198i	$-0.268123\pi$
$937$	40.7563			1.33145			0.665725	+	0.746198i	$0.268123\pi$
$938$		0			0
$939$	−5.23528	−	5.23528i	−0.170847	−	0.170847i
$940$		0			0
$941$	36.2143	−	36.2143i	1.18055	−	1.18055i	0.200950	−	0.979602i	$-0.435597\pi$
$941$	36.2143	−	36.2143i	1.18055	−	1.18055i	0.979602	−	0.200950i	$-0.0644027\pi$
$942$		0			0
$943$			14.6845i			0.478193i
$944$		0			0
$945$	−0.601657	+	1.46290i	−0.0195719	+	0.0475880i
$946$		0			0
$947$	36.5242	+	36.5242i	1.18688	+	1.18688i	0.977926	+	0.208951i	$0.0670050\pi$
$947$	36.5242	+	36.5242i	1.18688	+	1.18688i	0.208951	+	0.977926i	$0.432995\pi$
$948$		0			0
$949$	37.4738	+	37.4738i	1.21645	+	1.21645i
$950$		0			0
$951$			2.55566i			0.0828729i
$952$		0			0
$953$	−16.0927			−0.521294			−0.260647	−	0.965434i	$-0.583936\pi$
$953$	−16.0927			−0.521294			−0.260647	+	0.965434i	$0.583936\pi$
$954$		0			0
$955$	−36.7421	+	15.3272i	−1.18895	+	0.495975i
$956$		0			0
$957$	12.4699	+	12.4699i	0.403093	+	0.403093i
$958$		0			0
$959$	5.16423			0.166762
$960$		0			0
$961$	26.8716			0.866826
$962$		0			0
$963$	−9.49009	−	9.49009i	−0.305814	−	0.305814i
$964$		0			0
$965$	−14.8264	−	35.5416i	−0.477278	−	1.14413i
$966$		0			0
$967$	−21.3561			−0.686767			−0.343384	−	0.939195i	$-0.611573\pi$
$967$	−21.3561			−0.686767			−0.343384	+	0.939195i	$0.611573\pi$
$968$		0			0
$969$		−	0.532856i		−	0.0171178i
$970$		0			0
$971$	20.0626	+	20.0626i	0.643839	+	0.643839i	0.951497	−	0.307658i	$-0.0995454\pi$
$971$	20.0626	+	20.0626i	0.643839	+	0.643839i	−0.307658	+	0.951497i	$0.599545\pi$
$972$		0			0
$973$	−6.26414	−	6.26414i	−0.200819	−	0.200819i
$974$		0			0
$975$	19.4140	+	19.2202i	0.621747	+	0.615540i
$976$		0			0
$977$		−	27.7769i		−	0.888661i	−0.895863	−	0.444331i	$-0.853442\pi$
$977$		−	27.7769i		−	0.888661i	0.895863	−	0.444331i	$-0.146558\pi$
$978$		0			0
$979$	5.53447	−	5.53447i	0.176882	−	0.176882i
$980$		0			0
$981$	11.9058	+	11.9058i	0.380122	+	0.380122i
$982$		0			0
$983$	0.428090			0.0136540			0.00682698	−	0.999977i	$-0.497827\pi$
$983$	0.428090			0.0136540			0.00682698	+	0.999977i	$0.497827\pi$
$984$		0			0
$985$	12.1201	−	29.4694i	0.386179	−	0.938973i
$986$		0			0
$987$	−2.23763	+	2.23763i	−0.0712245	+	0.0712245i
$988$		0			0
$989$	−4.73871	+	4.73871i	−0.150682	+	0.150682i
$990$		0			0
$991$	5.82267			0.184963			0.0924816	−	0.995714i	$-0.470520\pi$
$991$	5.82267			0.184963			0.0924816	+	0.995714i	$0.470520\pi$
$992$		0			0
$993$			8.24078i			0.261513i
$994$		0			0
$995$	4.94303	+	11.8494i	0.156704	+	0.375650i
$996$		0			0
$997$	−20.1044	+	20.1044i	−0.636713	+	0.636713i	−0.949743	−	0.313030i	$-0.898656\pi$
$997$	−20.1044	+	20.1044i	−0.636713	+	0.636713i	0.313030	+	0.949743i	$0.398656\pi$
$998$		0			0
$999$		−	11.9906i		−	0.379366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bl.a.49.15		48
4.3	odd	2		240.2.bl.a.229.5	yes	48
5.4	even	2	inner	960.2.bl.a.49.9		48
8.3	odd	2		1920.2.bl.a.1249.18		48
8.5	even	2		1920.2.bl.b.1249.7		48
12.11	even	2		720.2.bm.h.469.20		48
16.3	odd	4		240.2.bl.a.109.20	yes	48
16.5	even	4		1920.2.bl.b.289.18		48
16.11	odd	4		1920.2.bl.a.289.7		48
16.13	even	4	inner	960.2.bl.a.529.9		48
20.19	odd	2		240.2.bl.a.229.20	yes	48
40.19	odd	2		1920.2.bl.a.1249.7		48
40.29	even	2		1920.2.bl.b.1249.18		48
48.35	even	4		720.2.bm.h.109.5		48
60.59	even	2		720.2.bm.h.469.5		48
80.19	odd	4		240.2.bl.a.109.5	✓	48
80.29	even	4	inner	960.2.bl.a.529.15		48
80.59	odd	4		1920.2.bl.a.289.18		48
80.69	even	4		1920.2.bl.b.289.7		48
240.179	even	4		720.2.bm.h.109.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.5	✓	48	80.19	odd	4
240.2.bl.a.109.20	yes	48	16.3	odd	4
240.2.bl.a.229.5	yes	48	4.3	odd	2
240.2.bl.a.229.20	yes	48	20.19	odd	2
720.2.bm.h.109.5		48	48.35	even	4
720.2.bm.h.109.20		48	240.179	even	4
720.2.bm.h.469.5		48	60.59	even	2
720.2.bm.h.469.20		48	12.11	even	2
960.2.bl.a.49.9		48	5.4	even	2	inner
960.2.bl.a.49.15		48	1.1	even	1	trivial
960.2.bl.a.529.9		48	16.13	even	4	inner
960.2.bl.a.529.15		48	80.29	even	4	inner
1920.2.bl.a.289.7		48	16.11	odd	4
1920.2.bl.a.289.18		48	80.59	odd	4
1920.2.bl.a.1249.7		48	40.19	odd	2
1920.2.bl.a.1249.18		48	8.3	odd	2
1920.2.bl.b.289.7		48	80.69	even	4
1920.2.bl.b.289.18		48	16.5	even	4
1920.2.bl.b.1249.7		48	8.5	even	2
1920.2.bl.b.1249.18		48	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-2.06370 + 0.860885i) q^{5} -0.707398 q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(-2.06370 + 0.860885i) q^{5} -0.707398 q^{7} +1.00000i q^{9} +(-1.79993 - 1.79993i) q^{11} +(3.86348 + 3.86348i) q^{13} +(-2.06800 - 0.850522i) q^{15} +0.244884i q^{17} +(-1.53863 + 1.53863i) q^{19} +(-0.500206 - 0.500206i) q^{21} -6.92280 q^{23} +(3.51775 - 3.55323i) q^{25} +(-0.707107 + 0.707107i) q^{27} +(-4.89882 + 4.89882i) q^{29} -7.60734 q^{31} -2.54548i q^{33} +(1.45986 - 0.608988i) q^{35} +(-8.47863 + 8.47863i) q^{37} +5.46378i q^{39} -2.12118i q^{41} +(0.684507 - 0.684507i) q^{43} +(-0.860885 - 2.06370i) q^{45} -4.47342i q^{47} -6.49959 q^{49} +(-0.173159 + 0.173159i) q^{51} +(1.47026 - 1.47026i) q^{53} +(5.26405 + 2.16499i) q^{55} -2.17595 q^{57} +(-5.86121 - 5.86121i) q^{59} +(0.0537432 - 0.0537432i) q^{61} -0.707398i q^{63} +(-11.2991 - 4.64706i) q^{65} +(7.85550 + 7.85550i) q^{67} +(-4.89516 - 4.89516i) q^{69} -2.08595i q^{71} +9.69951 q^{73} +(4.99994 - 0.0250827i) q^{75} +(1.27326 + 1.27326i) q^{77} +7.34690 q^{79} -1.00000 q^{81} +(6.80291 + 6.80291i) q^{83} +(-0.210817 - 0.505369i) q^{85} -6.92797 q^{87} +3.07483i q^{89} +(-2.73301 - 2.73301i) q^{91} +(-5.37920 - 5.37920i) q^{93} +(1.85069 - 4.49986i) q^{95} +1.39922i q^{97} +(1.79993 - 1.79993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{19} + 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} + 16 q^{61} + 16 q^{65} - 16 q^{69} + 16 q^{75} + 96 q^{79} - 48 q^{81} + 32 q^{91} + 48 q^{95}+O(q^{100}) \) 48 * q - 8 * q^19 + 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 + 16 * q^61 + 16 * q^65 - 16 * q^69 + 16 * q^75 + 96 * q^79 - 48 * q^81 + 32 * q^91 + 48 * q^95

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